Explanation/Reference:
Note:
A general outline of what needs to be done is as follows:
* (step 1, step 2) Create the new Exchange 2013 DAG and add Exchange 2013 mailbox servers to the DAG.
* (Step 3) Create mailbox database copies within the Exchange 2013 DAG as required.
* (Step 4) Move mailboxes from databases in the Exchange 2010 DAG to the Exchange 2013 DAG.
* (Step 5) We should move all the public folders last.
Note: Due to the changes in how public folders are stored, legacy Exchange mailboxes are unable to access the public folder hierarchy on Exchange 2013 servers or on Exchange Online. However, user mailboxes on Exchange 2013 servers or Exchange Online can connect to legacy public folders. Exchange
2013 public folders and legacy public folders can't exist in your Exchange organization simultaneously.
This effectively means that there's no coexistence between versions. Migrating public folders to Exchange Server 2013 or Exchange Online is currently a one-time cutover process.
For this reason, it's recommended that prior to migrating your public folders, you should first migrate your legacy mailboxes to Exchange 2013 or Exchange Online.
Reference: Migrating an Exchange 2010 DAG to Exchange 2013
http://windowsitpro.com/blog/migrating-exchange-2010-dag-exchange-2013
Reference: Public Folders
https://technet.microsoft.com/en-us/library/jj150538%28v=exchg.150%29.aspx